cp's OEIS Frontend

A346112 Size of the smallest regular polygon chain for a regular polygon with n sides.

%I A346112 #48 Jul 29 2023 03:22:07
%S A346112 6,4,6,3,6,4,6,5,6,3,6,4,6,4,6,3,6,4
%N A346112 Size of the smallest regular polygon chain for a regular polygon with n sides.
%C A346112 Each polygon in a polygon chain shares one edge with both its predecessor and successor polygon.  The polygon chain forms a connected cycle.
%H A346112 Stuart Anderson, <a href="http://www.squaring.net/polygons/polygon-chains.png"> Smallest regular polygon chains for n= 3 to 16</a>
%H A346112 Dan McKinnon, <a href="http://www.mathrecreation.com/2015/07/regular-polygons-in-rings.html">Regular polygons, in rings</a>
%F A346112 Empirical observations for n >= 3:
%F A346112 a(n) = 3 if n == 0 (mod 6),
%F A346112        4 if n == 4 or 8 (mod 12),
%F A346112        5 if n = 10,
%F A346112        4 if n = 14,
%F A346112        6 otherwise.
%e A346112 For n = 6, 3 hexagons can form a ring.  See the first link for this and further images.
%o A346112 (C++)
%o A346112 #include <iostream>
%o A346112 using namespace std;
%o A346112 int a(int n);
%o A346112 int main() {
%o A346112     int t = 30; //change to extend the number of terms
%o A346112     for (int n = 3; n < t; n++){
%o A346112         cout<< "n= "<<n<<" a(n)= "<<a(n)<<endl;
%o A346112     }
%o A346112     return 0;
%o A346112 }
%o A346112 int a(int n) {
%o A346112     int s =0;
%o A346112     if (n%6 == 0) {
%o A346112         s = 3;
%o A346112     } else if (n == 10) {
%o A346112         s = 5;
%o A346112     } else if (n == 14) {
%o A346112         s = 4;
%o A346112     } else if (n%4 == 0) {
%o A346112         s = 4;
%o A346112     } else {
%o A346112         s = 6;
%o A346112     }
%o A346112     return s;
%o A346112 }
%K A346112 nonn,more,hear
%O A346112 3,1
%A A346112 _Stuart E Anderson_, Jul 05 2021